Blender connected proportional edit in UV/Image editor not working
Unfortunately proportional editing in the UV editor works differently to the 3Dview. In the 3Dview connected proportional editing will only move vertices that are directly attached to the selected vertices that you are moving. In the UV editor all points that are indirectly connected are influenced by proportional editing.

A possible solution is to select only the vertices you want to move (in the 3Dview), the unselected vertices will not be visible in the UV editor and will not be moved when you move the nearby points. Note that this can tear apart neighbouring faces at the edge of the selection.